MP-PCA denoising for diffusion MRS data: promises and pitfalls

Uncertainty propagation in absolute metabolite quantification for in vivo MRS of the human brain

PURPOSE

Absolute spectral quantification is the standard method for deriving estimates of the concentration from metabolite signals measured using in vivo proton MRS (1 H-MRS). This method is often reported with minimum variance estimators, specifically the Cramér-Rao lower bound (CRLB) of the metabolite signal amplitude's scaling factor from linear combination modeling. This value serves as a proxy for SD and is commonly reported in MRS experiments. Characterizing the uncertainty of absolute quantification, however, depends on more than simply the CRLB. The uncertainties of metabolite-specific (T1m , T2m ), reference-specific (T1ref , T2ref ), and sequence-specific (TR , TE ) parameters are generally ignored, potentially leading to an overestimation of precision. In this study, the propagation of uncertainty is used to derive a comprehensive estimate of the overall precision of concentrations from an internal reference.

METHODS

The propagated uncertainty is calculated using analytical derivations and Monte Carlo simulations and subsequently analyzed across a set of commonly measured metabolites and macromolecules. The effect of measurement error from experimentally obtained quantification parameters is estimated using published uncertainties and CRLBs from in vivo 1 H-MRS literature.

RESULTS

The additive effect of propagated measurement uncertainty from applied quantification correction factors can result in up to a fourfold increase in the concentration estimate's coefficient of variation compared to the CRLB alone. A case study analysis reveals similar multifold increases across both metabolites and macromolecules.

CONCLUSION

The precision of absolute metabolite concentrations derived from 1 H-MRS experiments is systematically overestimated if the uncertainties of commonly applied corrections are neglected as sources of error.

Diffusion-weighted MR spectroscopy: Consensus, recommendations, and resources from acquisition to modeling

Brain cell structure and function reflect neurodevelopment, plasticity, and aging; and changes can help flag pathological processes such as neurodegeneration and neuroinflammation. Accurate and quantitative methods to noninvasively disentangle cellular structural features are needed and are a substantial focus of brain research. Diffusion-weighted MRS (dMRS) gives access to diffusion properties of endogenous intracellular brain metabolites that are preferentially located inside specific brain cell populations. Despite its great potential, dMRS remains a challenging technique on all levels: from the data acquisition to the analysis, quantification, modeling, and interpretation of results. These challenges were the motivation behind the organization of the Lorentz Center workshop on "Best Practices & Tools for Diffusion MR Spectroscopy" held in Leiden, the Netherlands, in September 2021. During the workshop, the dMRS community established a set of recommendations to execute robust dMRS studies. This paper provides a description of the steps needed for acquiring, processing, fitting, and modeling dMRS data, and provides links to useful resources.

Practical considerations of diffusion-weighted MRS with ultra-strong diffusion gradients

Introduction

Diffusion-weighted magnetic resonance spectroscopy (DW-MRS) offers improved cellular specificity to microstructure-compared to water-based methods alone-but spatial resolution and SNR is severely reduced and slow-diffusing metabolites necessitate higher b-values to accurately characterize their diffusion properties. Ultra-strong gradients allow access to higher b-values per-unit time, higher SNR for a given b-value, and shorter diffusion times, but introduce additional challenges such as eddy-current artefacts, gradient non-uniformity, and mechanical vibrations.

Methods

In this work, we present initial DW-MRS data acquired on a 3T Siemens Connectom scanner equipped with ultra-strong (300 mT/m) gradients. We explore the practical issues associated with this manner of acquisition, the steps that may be taken to mitigate their impact on the data, and the potential benefits of ultra-strong gradients for DW-MRS. An in-house DW-PRESS sequence and data processing pipeline were developed to mitigate the impact of these confounds. The interaction of TE, b-value, and maximum gradient amplitude was investigated using simulations and pilot data, whereby maximum gradient amplitude was restricted. Furthermore, two DW-MRS voxels in grey and white matter were acquired using ultra-strong gradients and high b-values.

Results

Simulations suggest T2-based SNR gains that are experimentally confirmed. Ultra-strong gradient acquisitions exhibit similar artefact profiles to those of lower gradient amplitude, suggesting adequate performance of artefact mitigation strategies. Gradient field non-uniformity influenced ADC estimates by up to 4% when left uncorrected. ADC and Kurtosis estimates for tNAA, tCho, and tCr align with previously published literature.

Discussion

In conclusion, we successfully implemented acquisition and data processing strategies for ultra-strong gradient DW-MRS and results indicate that confounding effects of the strong gradient system can be ameliorated, while achieving shorter diffusion times and improved metabolite SNR.

Denoising single MR spectra by deep learning: Miracle or mirage?

PURPOSE

The inherently poor SNR of MRS measurements presents a significant hurdle to its clinical application. Denoising by machine or deep learning (DL) was proposed as a remedy. It is investigated whether such denoising leads to lower estimate uncertainties or whether it essentially reduces noise in signal-free areas only.

METHODS

Noise removal based on supervised DL with U-nets was implemented using simulated 1 H MR spectra of human brain in two approaches: (1) via time-frequency domain spectrograms and (2) using 1D spectra as input. Quality of denoising was evaluated in three ways: (1) by an adapted fit quality score, (2) by traditional model fitting, and (3) by quantification via neural networks.

RESULTS

Visually appealing spectra were obtained; hinting that denoising is well-suited for MRS. However, an adapted denoising score showed that noise removal is inhomogeneous and more efficient for signal-free areas. This was confirmed by quantitative analysis of traditional fit results as well as DL quantitation following DL denoising. DL denoising, although apparently successful as judged by mean squared errors, led to substantially biased estimates in both implementations.

CONCLUSION

The implemented DL-based denoising techniques may be useful for display purposes, but do not help quantitative evaluations, confirming expectations based on estimation theory: Cramér Rao lower bounds defined by the original data and the appropriate fitting model cannot be circumvented in an unbiased way for single data sets, unless additional prior knowledge can be incurred in the form of parameter restrictions/relations or applicable substates.

Singular vectors of sums of rectangular random matrices and optimal estimation of high-rank signals: The extensive spike model

Across many disciplines spanning from neuroscience and genomics to machine learning, atmospheric science, and finance, the problems of denoising large data matrices to recover hidden signals obscured by noise, and of estimating the structure of these signals, is of fundamental importance. A key to solving these problems lies in understanding how the singular value structure of a signal is deformed by noise. This question has been thoroughly studied in the well-known spiked matrix model, in which data matrices originate from low-rank signal matrices perturbed by additive noise matrices, in an asymptotic limit where matrix size tends to infinity but the signal rank remains finite. We first show, strikingly, that the singular value structure of large finite matrices (of size ∼1000) with even moderate-rank signals, as low as 10, is not accurately predicted by the finite-rank theory, thereby limiting the application of this theory to real data. To address these deficiencies, we analytically compute how the singular values and vectors of an arbitrary high-rank signal matrix are deformed by additive noise. We focus on an asymptotic limit corresponding to an extensive spike model, in which both the signal rank and the size of the data matrix tend to infinity at a constant ratio. We map out the phase diagram of the singular value structure of the extensive spike model as a joint function of signal strength and rank. We further exploit these analytics to derive optimal rotationally invariant denoisers to recover the hidden high-rank signal from the data, as well as optimal invariant estimators of the signal covariance structure. Our extensive-rank results yield several conceptual differences compared to the finite-rank case: (1) as signal strength increases, the singular value spectrum does not directly transition from a unimodal bulk phase to a disconnected phase, but instead there is a bimodal connected regime separating them; (2) the signal singular vectors can be partially estimated even in the unimodal bulk regime, and thus the transitions in the data singular value spectrum do not coincide with a detectability threshold for the signal singular vectors, unlike in the finite-rank theory; (3) signal singular values interact nontrivially to generate data singular values in the extensive-rank model, whereas they are noninteracting in the finite-rank theory; and (4) as a result, the more sophisticated data denoisers and signal covariance estimators we derive, which take into account these nontrivial extensive-rank interactions, significantly outperform their simpler, noninteracting, finite-rank counterparts, even on data matrices of only moderate rank. Overall, our results provide fundamental theory governing how high-dimensional signals are deformed by additive noise, together with practical formulas for optimal denoising and covariance estimation.

Mapping tissue microstructure across the human brain on a clinical scanner with soma and neurite density image metrics

Soma and neurite density image (SANDI) is an advanced diffusion magnetic resonance imaging biophysical signal model devised to probe in vivo microstructural information in the gray matter (GM). This model requires acquisitions that include b values that are at least six times higher than those used in clinical practice. Such high b values are required to disentangle the signal contribution of water diffusing in soma from that diffusing in neurites and extracellular space, while keeping the diffusion time as short as possible to minimize potential bias due to water exchange. These requirements have limited the use of SANDI only to preclinical or cutting-edge human scanners. Here, we investigate the potential impact of neglecting water exchange in the SANDI model and present a 10-min acquisition protocol that enables to characterize both GM and white matter (WM) on 3 T scanners. We implemented analytical simulations to (i) evaluate the stability of the fitting of SANDI parameters when diminishing the number of shells; (ii) estimate the bias due to potential exchange between neurites and extracellular space in such reduced acquisition scheme, comparing it with the bias due to experimental noise. Then, we demonstrated the feasibility and assessed the repeatability and reproducibility of our approach by computing microstructural metrics of SANDI with AMICO toolbox and other state-of-the-art models on five healthy subjects. Finally, we applied our protocol to five multiple sclerosis patients. Results suggest that SANDI is a practical method to characterize WM and GM tissues in vivo on performant clinical scanners.

Artificial intelligence for diffusion MRI-based tissue microstructure estimation in the human brain: an overview

Artificial intelligence (AI) has made significant advances in the field of diffusion magnetic resonance imaging (dMRI) and other neuroimaging modalities. These techniques have been applied to various areas such as image reconstruction, denoising, detecting and removing artifacts, segmentation, tissue microstructure modeling, brain connectivity analysis, and diagnosis support. State-of-the-art AI algorithms have the potential to leverage optimization techniques in dMRI to advance sensitivity and inference through biophysical models. While the use of AI in brain microstructures has the potential to revolutionize the way we study the brain and understand brain disorders, we need to be aware of the pitfalls and emerging best practices that can further advance this field. Additionally, since dMRI scans rely on sampling of the q-space geometry, it leaves room for creativity in data engineering in such a way that it maximizes the prior inference. Utilization of the inherent geometry has been shown to improve general inference quality and might be more reliable in identifying pathological differences. We acknowledge and classify AI-based approaches for dMRI using these unifying characteristics. This article also highlighted and reviewed general practices and pitfalls involving tissue microstructure estimation through data-driven techniques and provided directions for building on them.

MP-PCA denoising of fMRI time-series data can lead to artificial activation "spreading"

MP-PCA denoising has become the method of choice for denoising MRI data since it provides an objective threshold to separate the signal components from unwanted thermal noise components. In rodents, thermal noise in the coils is an important source of noise that can reduce the accuracy of activation mapping in fMRI. Further confounding this problem, vendor data often contains zero-filling and other post-processing steps that may violate MP-PCA assumptions. Here, we develop an approach to denoise vendor data and assess activation "spreading" caused by MP-PCA denoising in rodent task-based fMRI data. Data was obtained from N = 3 mice using conventional multislice and ultrafast acquisitions (1 s and 50 ms temporal resolution, respectively), during visual stimulation. MP-PCA denoising produced SNR gains of 64% and 39% and Fourier Spectral Amplitude (FSA) increases in BOLD maps of 9% and 7% for multislice and ultrafast data, respectively, when using a small [2 2] denoising window. Larger windows provided higher SNR and FSA gains with increased spatial extent of activation that may or may not represent real activation. Simulations showed that MP-PCA denoising can incur activation "spreading" with increased false positive rate and smoother functional maps due to local "bleeding" of principal components, and that the optimal denoising window for improved specificity of functional mapping, based on Dice score calculations, depends on the data's tSNR and functional CNR. This "spreading" effect applies also to another recently proposed low-rank denoising method (NORDIC), although to a lesser degree. Our results bode well for enhancing spatial and/or temporal resolution in future fMRI work, while taking into account the sensitivity/specificity trade-offs of low-rank denoising methods.